TSTP Solution File: REL031-2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : REL031-2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:48:35 EDT 2023
% Result : Unsatisfiable 43.16s 7.23s
% Output : Refutation 43.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of formulae : 106 ( 72 unt; 10 typ; 0 def)
% Number of atoms : 128 ( 127 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 804 ( 63 ~; 32 |; 0 &; 709 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 118 ( 0 ^; 118 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_type,type,
join: $i > $i > $i ).
thf(composition_type,type,
composition: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(one_type,type,
one: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(zero_type,type,
zero: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(top_type,type,
top: $i ).
thf(16,axiom,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
thf(51,plain,
! [A: $i] :
( top
= ( join @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(52,plain,
! [A: $i] :
( ( join @ A @ ( complement @ A ) )
= top ),
inference(lifteq,[status(thm)],[51]) ).
thf(6,axiom,
! [A: $i] :
( ( composition @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
thf(31,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
! [A: $i] :
( ( composition @ A @ one )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(3,negated_conjecture,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
thf(22,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(26,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one ),
inference(lifteq,[status(thm)],[25]) ).
thf(77,plain,
! [A: $i] :
( ( ( join @ A @ one )
!= one )
| ( ( composition @ A @ one )
!= ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,26]) ).
thf(81,plain,
! [A: $i] :
( ( ( join @ A @ one )
!= one )
| ( A
!= ( converse @ ( composition @ sk1 @ sk2 ) ) )
| ( ( composition @ sk1 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[77]) ).
thf(85,plain,
( ( ( join @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ one )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[81]) ).
thf(9,axiom,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
thf(37,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,plain,
! [A: $i] :
( ( converse @ ( converse @ A ) )
= A ),
inference(lifteq,[status(thm)],[37]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( converse @ ( composition @ A @ B ) )
= ( composition @ ( converse @ B ) @ ( converse @ A ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(812,plain,
! [C: $i,B: $i,A: $i] :
( ( ( converse @ A )
= ( composition @ ( converse @ C ) @ ( converse @ B ) ) )
| ( ( composition @ A @ one )
!= ( composition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[32,40]) ).
thf(813,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ ( converse @ A ) )
= ( converse @ A ) ),
inference(pattern_uni,[status(thm)],[812:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( one ))]]) ).
thf(951,plain,
! [B: $i,A: $i] :
( ( ( composition @ ( converse @ one ) @ A )
= ( converse @ B ) )
| ( ( converse @ ( converse @ A ) )
!= ( converse @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38,813]) ).
thf(952,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ A )
= ( converse @ ( converse @ A ) ) ),
inference(pattern_uni,[status(thm)],[951:[bind(A,$thf( C )),bind(B,$thf( converse @ C ))]]) ).
thf(1016,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ A )
= ( converse @ ( converse @ A ) ) ),
inference(simp,[status(thm)],[952]) ).
thf(1140,plain,
! [A: $i] :
( ( composition @ ( converse @ one ) @ A )
= A ),
inference(rewrite,[status(thm)],[1016,38]) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( composition @ ( converse @ one ) @ A )
!= ( composition @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[1140,32]) ).
thf(1159,plain,
( ( converse @ one )
= one ),
inference(pattern_uni,[status(thm)],[1158:[bind(A,$thf( one )),bind(B,$thf( converse @ one ))]]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( join @ ( composition @ ( converse @ A ) @ ( complement @ ( composition @ A @ B ) ) ) @ ( complement @ B ) )
= ( complement @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,negated_conjecture,
( ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
thf(21,plain,
( ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
( ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one )
= one ),
inference(lifteq,[status(thm)],[21]) ).
thf(73,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one ) ),
inference(paramod_ordered,[status(thm)],[24,26]) ).
thf(82,plain,
( ( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk2 ) @ sk2 ) )
| ( one != one ) ),
inference(simp,[status(thm)],[73]) ).
thf(86,plain,
( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk2 ) @ sk2 ) ),
inference(simp,[status(thm)],[82]) ).
thf(202,plain,
( ( ( converse @ ( composition @ sk1 @ sk2 ) )
!= ( converse @ sk2 ) )
| ( ( composition @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[86]) ).
thf(751,plain,
( ( ( composition @ sk1 @ sk2 )
!= sk2 )
| ( ( composition @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[202]) ).
thf(774,plain,
( ( composition @ sk1 @ sk2 )
!= sk2 ),
inference(simp,[status(thm)],[751]) ).
thf(1151,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( composition @ ( converse @ one ) @ A )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1140,774]) ).
thf(1185,plain,
( ( ( converse @ one )
!= sk1 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[1151]) ).
thf(1223,plain,
( ( converse @ one )
!= sk1 ),
inference(simp,[status(thm)],[1185]) ).
thf(1293,plain,
one != sk1,
inference(rewrite,[status(thm)],[1223,1159]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ A @ ( join @ B @ C ) )
= ( join @ ( join @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ A @ ( composition @ B @ C ) )
= ( composition @ ( composition @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1252,plain,
( ( ( join @ one @ one )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= one )
| ( ( converse @ ( composition @ sk1 @ sk2 ) )
!= ( converse @ one ) ) ),
inference(paramod_ordered,[status(thm)],[1159,85]) ).
thf(1285,plain,
( ( ( join @ one @ one )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[1252]) ).
thf(1288,plain,
( ( ( join @ one @ one )
!= one )
| ( ( composition @ sk1 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[1285]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( converse @ ( join @ A @ B ) )
= ( join @ ( converse @ A ) @ ( converse @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( join @ A @ B )
= ( join @ B @ A ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(1,negated_conjecture,
( ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
thf(20,plain,
( ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( meet @ A @ B )
= ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) )
= ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_2_16) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) )
= ( meet @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
( ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one )
= one ),
inference(lifteq,[status(thm)],[20]) ).
thf(78,plain,
( ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one )
!= ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one ) ),
inference(paramod_ordered,[status(thm)],[23,26]) ).
thf(79,plain,
( ( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk1 ) @ sk1 ) )
| ( one != one ) ),
inference(simp,[status(thm)],[78]) ).
thf(89,plain,
( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )
!= ( composition @ ( converse @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[79]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
thf(33,plain,
! [B: $i,A: $i] :
( A
= ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1246,plain,
! [A: $i] :
( ( composition @ one @ A )
= A ),
inference(rewrite,[status(thm)],[1140,1159]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( join @ ( complement @ ( join @ ( complement @ A ) @ ( complement @ B ) ) ) @ ( complement @ ( join @ ( complement @ A ) @ B ) ) )
= A ),
inference(lifteq,[status(thm)],[33]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( composition @ A @ B ) @ C )
= ( composition @ A @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(4,axiom,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
thf(27,plain,
! [A: $i] :
( zero
= ( meet @ A @ ( complement @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law_14) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) )
= ( composition @ ( meet @ A @ ( composition @ C @ ( converse @ B ) ) ) @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(242,plain,
! [A: $i] :
( ( ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ A )
!= ( composition @ ( converse @ sk1 ) @ sk1 ) )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[32,89]) ).
thf(265,plain,
! [A: $i] :
( ( ( converse @ ( composition @ sk1 @ sk2 ) )
!= ( converse @ sk1 ) )
| ( A != sk1 )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[242]) ).
thf(273,plain,
( ( ( converse @ ( composition @ sk1 @ sk2 ) )
!= ( converse @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[265]) ).
thf(280,plain,
! [A: $i] :
( ( ( converse @ A )
!= ( converse @ sk1 ) )
| ( sk2 != one )
| ( ( composition @ A @ one )
!= ( composition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[32,273]) ).
thf(285,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk2 != one )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[280]) ).
thf(295,plain,
sk2 != one,
inference(simp,[status(thm)],[285]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
!= one )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[42,26]) ).
thf(327,plain,
( ( join @ one @ ( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) ) )
!= one ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( composition @ ( converse @ ( composition @ sk1 @ sk2 ) ) @ ( composition @ sk1 @ sk2 ) )),bind(B,$thf( one ))]]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= one )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( converse @ sk1 ) @ sk1 ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[42,23]) ).
thf(331,plain,
( ( join @ one @ ( composition @ ( converse @ sk1 ) @ sk1 ) )
= one ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( composition @ ( converse @ sk1 ) @ sk1 )),bind(B,$thf( one ))]]) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( join @ C @ B )
= top )
| ( ( join @ A @ ( complement @ A ) )
!= ( join @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[52,42]) ).
thf(299,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( complement @ D ))]]) ).
thf(338,plain,
! [A: $i] :
( ( join @ ( complement @ A ) @ A )
= top ),
inference(simp,[status(thm)],[299]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( join @ B @ A )
= one )
| ( ( join @ A @ B )
!= ( join @ ( composition @ ( converse @ sk2 ) @ sk2 ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[42,24]) ).
thf(319,plain,
( ( join @ one @ ( composition @ ( converse @ sk2 ) @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( composition @ ( converse @ sk2 ) @ sk2 )),bind(B,$thf( one ))]]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) )
= ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1_15) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( meet @ ( composition @ A @ B ) @ C ) @ ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) )
= ( meet @ ( composition @ A @ ( meet @ B @ ( composition @ ( converse @ A ) @ C ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( join @ ( join @ A @ B ) @ C )
= ( join @ A @ ( join @ B @ C ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( composition @ ( join @ A @ B ) @ C )
= ( join @ ( composition @ A @ C ) @ ( composition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(17164,plain,
$false,
inference(e,[status(thm)],[52,85,1159,53,39,1293,35,43,1288,47,42,24,37,20,46,57,29,774,89,38,21,33,1246,41,45,32,34,22,44,27,49,86,295,327,331,338,31,319,40,26,55,23,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : REL031-2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Thu May 18 18:03:20 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.63/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.82 % [INFO] Parsing done (114ms).
% 0.91/0.82 % [INFO] Running in sequential loop mode.
% 1.40/1.02 % [INFO] eprover registered as external prover.
% 1.40/1.03 % [INFO] cvc4 registered as external prover.
% 1.40/1.03 % [INFO] Scanning for conjecture ...
% 1.40/1.09 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.62/1.12 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.62/1.15 % [INFO] Problem is propositional (TPTP CNF).
% 1.62/1.15 % [INFO] Type checking passed.
% 1.62/1.15 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 43.16/7.22 % External prover 'e' found a proof!
% 43.16/7.22 % [INFO] Killing All external provers ...
% 43.16/7.22 % Time passed: 6839ms (effective reasoning time: 6396ms)
% 43.16/7.22 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 43.16/7.22 % Axioms used in derivation (16): maddux3_a_kind_of_de_Morgan_3, converse_idempotence_8, def_top_12, converse_cancellativity_11, composition_associativity_5, maddux2_join_associativity_2, composition_distributivity_7, maddux1_join_commutativity_1, modular_law_1_15, composition_identity_6, maddux4_definiton_of_meet_4, converse_additivity_9, dedekind_law_14, modular_law_2_16, def_zero_13, converse_multiplicativity_10
% 43.16/7.22 % No. of inferences in proof: 96
% 43.16/7.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6839 ms resp. 6396 ms w/o parsing
% 43.16/7.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.16/7.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------